Continuous-time filters have become widely used in commercial applications. Currently, this area is dominated by transconductor-capacitor (gm-C) filters. However, in low and medium frequency applications the active RC filters feature higher dynamic range and lower distortion. Active RC filters are constructed from resistors, capacitors, and integrated amplifiers. A basic building block is an integrator comprising an op-amp with an input resistor and a feedback capacitor. For low to medium frequency applications, the amplifiers can be treated as having essentially infinite gain and input impedance. Because little or no current is drawn by the amplifiers, the amplifier inputs function as virtual grounds and substantially all of the input signal is applied to the resistors and capacitors. Thus, the operating characteristics of the filter are determined by the various RC products.
In some situations, it has proven useful to provide a feedback amplifier in series with a compensating feedback capacitor. For example, a unity gain amplifier placed in the feedback path has been used to improve stability of MOS amplifier circuits. Y. P. Tsividis, "Single-Channel MOS Analog IC's," IEEE Journal of Solid-State Circuits, Vol. SC-13, No. 3, pp. 389-90, June 1978. A non-tunable amplifier with gain less than or equal to 1 has also been used in phase-lead integrators to cancel out "errors" in the quality factor. Q. K. Martin and A. S. Sedra, "On the Stability of the Phase-Lead Integrator," IEEE Trans. Circuits Syst., Vol. CAS-24, pp. 321-324, June 1977. According to theory, making the unity-gain bandwidth of the main and feedback amplifiers identical results in a value of Q which approaches infinity. Thus, attempts to improve Q in this manner used matched circuits for the main and feedback amplifiers. In practice, however, non-ideal aspects of the circuits cause the integrator to oscillate.
Another drawback to using active integrated RC filters is the variation of the RC product of up to +/-50% from its nominal value due to process and temperature variations. Tuning of the frequency response of the filter to compensate for this variation remains the main problem in VLSI implementation. Although, as discussed above, feedback amplifiers have been used to improve performance, they have not been used to achieve a tunable filter. Instead, there are three conventional approaches to implementing monolithic active RC filters: MOSFET-C, R-MOSFET-C, and R-C Array. In MOSFET-C filters, the resistors are replaced by MOSFETS devices that can be tuned via gate terminals. The R-MOSFET-C approach improves linearity of the MOSFET-C technique by inserting resistors in series with the MOSFETS. However, this technique also degrades the noise performance of the filter. The third approach, R-C Array, achieves the highest dynamic range reported so far by using resistors and replacing capacitors with capacitor arrays which are tuned with a digital signal whose value is set during an initial tuning cycle. A filter using capacitor arrays is especially useful in low-noise high-linearity applications.
However, the major disadvantage with the capacitor array approach is that the capacitor arrays require significant area. This is becoming more important with advances in silicon technology. As the active areas of the transistors decrease, the area required to fabricate the active circuits such as amplifiers and bias circuits shrink. However, there has been little improvement in on-chip capacitor density. As a result, the area of continuous time filters is increasingly dominated by the capacitance size. Another disadvantage of the capacitor array approach is that a filter utilizing capacitor arrays cannot operate while it is being tuned.